1. Field of the Invention
The present invention relates generally to three phase power transmission, and more specifically to an inductance balancer for three phase power transmission over a flat cable.
2. Description of the Prior Art
Three phase power transmission generally employs separate conductors for each phase. The conductors within a three phase cable are generally in relatively close proximity, giving rise to inductive effects between each current carrying conductor and the remaining conductors. The instantaneous current in each of the three conductors varies with the current phase: at one instant, current is carried on one conductor and returned on a second while current within the third conductor is zero; at other times during the cycle, current is carried on one conductor and returned in equal parts on the other two conductors. The current changes result in corresponding changes in inductance between the conductors.
For this reason, round cables, in which each conductor as seen from a cross-section is spaced an equal distance from the other two at the apex of an equilateral triangle, are generally preferred for three phase power transmission. Some apparently believe that, due to geometry, total inductance remains unchanged as current varies between the two instantaneous values described above (i.e., zero current in one phase with current carried and returned in the remaining two phases versus current carried in one phase and returned equally on the remaining two phases). In fact, total inductance varies significantly with the current phase. However, as current changes throughout a phase cycle, the total cable inductance moves through a repetitive cycle. Since the cable is round and symmetric, each conductor goes through identical cycles. The total inductance of the cable moves through 6 peaks and valleys as the current goes through one complete line frequency cycle so that each phase, while not constant in inductance, presents the same inductance cycle between source and load and therefore the root-mean-square (RMS) currents remain balanced.
Flat three phase cables, in which the conductors as seen from a cross-section all lie within a common plane, are known to imbalance RMS currents. Flat cable causes current imbalance primarily due to differing inductance characteristics for the three conductors in the cable. Some degree of resistive imbalance may exist due to the slightly higher temperature of the center conductor, but this effect is completely overshadowed by the inductive behavior. Upon analyzing a three phase system with an inductive load which is driven through three inductors including one with lower inductance than the other two, current on the phase with the smaller inductance will be found to be highest, with the lowest current found on the leading phase (with respect to the phase having the smallest inductance) and current on the lagging phase falling somewhere in between. Similar analysis with resistors in place of inductors, with the resistance on one phase being greater than on the other two, shows that the high resistance phase will have the middle level current, with the lagging phase having the highest current and the leading phase again having the lowest current. The magnitude of these effects determined by analysis and measurement of flat cable current shows that the inductance is the unbalancing factor when flat cable is utilized for three phase power transmission.
When flat cable is utilized to drive a three phase motor, the differing conductor inductances cause small changes in the voltage amplitude and phase at the motor terminals. The small differences in voltages are known to cause relatively large differences in phase currents, with those unbalances causing additional voltage drops and worsening the unbalance until an equilibrium is reached. Use of long lengths (5,000 to 8,000 feet) of flat cable to drive a three phase motor may thus result in current unbalance on the order of 10 to 15 percent. Additionally, in most applications, drives are sized closely to the required power (kilo-volt ampere or KVA)xe2x80x94that is, the drive output current capability is sized close to the current needed by the motor. Even if the drive can produce more current, exceeding the motor nameplate current is usually avoided by setting the current limit of the drive. In either case, when flat cable it utilized, one phase will reach the current limit before the other two, at which time the drive will cease to increase in frequency and the pump will operated at a lower RPM than desired. Accordingly, conductor inductance differences may result in significant voltage and current unbalances at the motor terminals and limit drive frequency.
In many applications, such as downhole motor applications where casing and tubing dimensions do not leave enough room for round cable, use of flat cable is imperative. In addition to dimensional considerations, logistics or splicing concerns may drive the use of flat cable. Many reasons, each having validity, may prompt the use of flat cable for three phase power transmission rather than round cable, and thus current imbalances are frequently encountered.
Several means of current balancing have been used or attempted, the simplest of which is transposition of conductors such that each phase is on the center conductor for equal cable lengths. This technique is often utilized for surface power lines and is also applicable to ESP applications. However, transposition splices often become large, and in some cases no room for the splice exists while in other cases the transpositions splices are a source of installation difficulty or the source of concern associated with having any additional splices.
It would be desirable, therefore, to provide a mechanism for balancing current in flat cables employed for three phase power transmission. It would also be advantageous for the mechanism to balance inductance.
An inductance balancer is connected between a power source and a flat three phase power transmission cable employed to carry power to a remote load. The inductance balancer includes a first inductance device (e.g., a single wound inductor) connecting the center cable conductor to the drive and raising the total effective inductance of the center cable conductor to the inductance of either of the outer cable conductors at maximum inductance. The inductance balancer also includes a second inductance device connecting both outer conductors to the drive and adding an inductance equal to that of the first inductance device when current exists only on an outer conductor and the center conductor, but adding no inductance to the outer conductors when current exists only on those two conductors. The second inductance device may be a dual wound inductor with each series connected to an outer conductor so that current carried or returned by one outer conductor travels through the inductor in an opposite direction to current carried or returned by the opposite outer conductor. The inductances resulting from equal currents on the outer conductors is zero because of the magnetic fields cancel, but the inductance resulting from currents in only one outer conductor and the center conductor is full value. The result is a degree of equalization of total inductance on all conductors for all current phasings, removing the flat cable characteristics from the system.